Generates a Hankel matrix.
HANKEL(c, r)
c |
- |
A series, the first column of the output array. |
r |
- |
Optional. A series, the last row of the output array. If not specified, the first element of the last row equals the last column value and the remaining values are all 0. |
An array, a Hankel matrix.
c = {1, 2, 3};
h = hankel(c);
h == {{1, 2, 3},
{2, 3, 0},
{3, 0, 0}}
The first row and column of h is identical to c.
c = {1, 2, 3};
r = {3, 8, 9};
h = hankel(c, r);
h == {{1, 2, 3},
{2, 3, 8},
{3, 8, 9}}
The last row is identical to r and the first column is identical to c.
For column c and row r, a Hankel matrix takes the form:
c[1] c[2] c[3] ... r[1]
c[2] r[1] r[1] ... r[2]
c[3] r[2] r[2] ... r[3]
. . . . .
. . . . .
. . . . .
c[n] r[n-2] r[n-1] ... r[n]
If r is not specified, a square Hankel matrix is returned where c represents the first row and column. The elements below the first anti-diagonal are zero such that:
If r is specified, an unsymmetric Hankel matrix is returned where the first column is c and the last row is r such that:
In this case, if c[end] ≠ r[1], c[end] is used as the last element.